Question

The sum of n terms of the sequence 3,9,15,21 is 7500 determine value if n

Answer 1

To find the value of n, we need to determine the pattern of the sequence and then find the general formula for the nth term.

From 3 to 9, we add 6.
From 9 to 15, we add 6.
From 15 to 21, we add 6.

Therefore, the sequence has a common difference of 6.

The formula for the nth term of an arithmetic sequence is given by: tn = a + (n - 1)d, where a is the first term and d is the common difference.

In this case, the formula is: tn = 3 + (n - 1)6.

Now, we need to find the value of n when the sum of the sequence is 7500.

The sum of an arithmetic series is given by the formula: Sn = (n/2)(a + tn), where Sn is the sum of the first n terms.

In this case, Sn = 7500 and a = 3. Substituting the values into the formula:

7500 = (n/2)(3 + (3 + (n - 1)6))
7500 = (n/2)(3 + 3 + 6n - 6)
7500 = (n/2)(6n)
7500 = 3n^2
2500 = n^2
n = √2500
n = 50 or n = -50

Since n represents the number of terms in the sequence, it cannot be negative. Therefore, the value of n is 50.